Future cash flows and buying a car

- Now you and your family moved to Hong Kong in 1995. - We did, we lived there for three years. - Did you buy a car while you were there? - No, but we actually did some financial analysis to determine whether we should buy a car. - What kind of analysis? - Well, basically we did a discounted cashflow analysis, a DCF. We forecasted the amount and timing of cash flows, used an interest rate and estimated what a car would be worth to us. - Well, tell us some of the numbers you used. - Okay, well now, I'll convert these numbers into US dollars for you, but of course the original analysis was done in Hong Kong dollars. We estimated that we would receive about $1,200 in net annual savings in terms of our higher spending on public transportation costs, compared to the lower cost of operating the car, gasoline, maintenance, taxes, insurance. - Wow, you must've been spending a lot on public transportation. - (laughs) We were. On weekends, we liked to take family trips to see the sights in Hong Kong. I've taken you to see some of those sights in Hong Kong. - True that. - Because there were six of us, if we took a taxi, we had to get two taxis. Only five people could fit into one taxi. - What about buses and subways? - Well, yeah, the bus system and the subway system in Hong Kong are great, but it costs quite a bit to travel around town on public transportation with six people. - Okay, so what was your planning horizon? - Well, we decided we should do our analysis based on using the car for five years, and we simplified the calculations by making the standard assumption that the savings of $1,200 per year would occur at the end of the year. Again, this was just to keep things simple. - Okay, here's what we know so far. A car will save you $1,200 at the end of each year for five years. That is the amount and timing of the cash flows. But in order to complete this discounted cashflow analysis, we need an interest rate. - Yeah, well we just use 10%. It's a standard rate. We didn't do any risk adjustment to the interest rate. - And we'll talk about risk adjusted interest rates in another module. Okay, savings of $1,200 per year at the end of each year for five years, an interest rate of 10%, by putting these numbers together in a discounted cashflow analysis, you can figure out how much the car was worth to you. - Yeah, yeah, exactly. We did this calculation in a calculator. PMT, $1,200, that's the payment amount, which is the annual savings in this example. I, 10%, that's the annual interest rate. N equals five, that's the number of years. And our answer was a PV, present value, $4,549. The present value is the value today of the five years of future cash savings. So we figured that a car would be worth $4,549 to us. - Okay, great. What was the price of the cars you were looking at? - We found a pretty inexpensive car for a little over $5,000. - So using discounted cash flow analysis, you estimated that the value of the car to you was $4,549 but the actual price to buy the car was $5,000. Okay, so what'd you do? Did you buy the car? - No, it costs more than the present value of the future cash savings. - And there you go, ladies and gentlemen, discounted cashflow analysis in action.